Logarithmic Theory Research Articles

Turbulence, Sediment‐Induced Stratification, and Mixing Under Macrotidal Estuarine Conditions (Qiantang Estuary, China)

AbstractTime series of in situ measured velocity and suspended sediment concentration from Qiantang Estuary (China), and estimates of turbulence and sediment stratification parameters are presented. The data span a period of 9 days, and after phase averaged, they are used to explore spring‐neap tidal variations in flow, turbulence, and sediment stratification. A local balance between shear production, sediment‐induced buoyancy flux, and dissipation is found to hold during ebb for both neap and spring tides. During flood elevated turbulence dissipation rates are observed, attributed to nonlocal turbulence, most likely due to horizontal advection. Our results show that the effect of sediment stratification is successfully parameterized by adding the Monin‐Obukhov length scale to the classical logarithmic layer theory. Flood‐ebb asymmetry in both Rig and Rf is observed, with higher values attained during flood due to the higher sediment concentrations and the corresponding weaker velocity shear found at these times. Rf is found to increase with Rig when Rig < 0.25, and it attains a maximum value of ~0.2. Our estimates, consistently with those from previous studies, fall slightly below the commonly used theoretical predictions. Sediment stratification contributes to the decay of turbulence, and weak mixing still exists under high Rig numbers.

Flow structure within a vegetation patch in a gravel-bed river

Abstract Investigation of the interactions between submerged vegetation patch and flow structure is of crucial importance for river engineering. Most of hydraulic models have been presented for fully developed flows over uniform vegetation in the laboratory conditions; however, the mentioned interactions are complex in river flows where the flow is not developed along small patch. This reveals a gap between developed and non-developed flow along the vegetation patch. This study was conducted in a gravel-bed river in the central Iran. The results reveal that the flow structure in evolving flow (non-developed flow) along the patch resembles that in shallow mixing layer. Accordingly, a shallow mixing layer model and modified equations are combined to quantify evolving area along the patch. The evolving shallow mixing layer equations for the flow along a non-uniform vegetation patch reach a reasonable agreement with field data. However, the spreading coefficient of this model less than one was reported in literature, 0.06 and 0.12. In addition, the flow immediately downstream the vegetation patch behaves similar to a jet and is parameterized by two conventional models, conventional logarithmic law and mixing layer theory. These models present a reasonable agreement with the measured velocity profiles immediately downstream the patch.

A finite strain incremental-secant homogenization model for elasto-plastic composites

This paper presents a finite strain extension of the incremental-secant mean-field homogenization (MFH) formulation for two-phase elasto-plastic composites. The formulation of the local finite strain elasto-plastic constitutive equations of each phase is based on a multiplicative decomposition of the deformation gradient as suggested by Simo in (Computer Methods in Applied Mechanics and Engineering, 99(1):61–112, 1992.). The latter has proposed algorithms which preserve the classical return mapping schemes of the infinitesimal theory by using principal Kirchhoff stresses and logarithmic eigenvalues of the left elastic Cauchy–Green strain. Relying on this property, we show that, by considering a quadratic logarithmic free energy and J2-flow theory at the local level, infinitesimal strain incremental-secant MFH is readily extended to finite strains. The proposed formulation and corresponding numerical algorithms are then presented. Finally, the predictions are illustrated with several numerical simulations which are verified against full-field finite element simulations of composite cells, demonstrating that the micro-mechanically based approach is able to predict the influence of the micro-structure and of its evolution on the macroscopic properties in a very cost-effective manner.

Flow structure in large bedrock‐channels: The example of macroturbulent rapids, lower Mekong River, Southeast Asia

AbstractThe rate of bedrock channel incision is key to the understanding of landscape evolution. Theoretical models relate channel incision to sediment transport; the latter conditioned by the bed shear stress. However, theory is deficient in an appreciation of the transverse and vertical flow structure that mediates shear stress for deep, narrow inner‐channels, which often characterize large bedrock rivers. Here we present the detail of the structure of high Reynolds number flows for bedrock‐controlled rapids of the Mekong River, SE Asia. Distinct filaments of high‐velocity flow, separated by regions of slower flow, occur across channels; the numbers of filaments scale linearly with channel width to maximum‐depth (B/hmax) ratios. Inner‐channels with low ratios (B/hmax < 20) exhibit wall‐effected flow structure. Effects include suppressed maximum velocity filaments due to: (i) significant channel‐transverse flow; (ii) strongly‐sheared vertical flow structure; and (iii) significant underflows. Such complex water column flow patterns largely defy theoretical description. Nonetheless near the bed, the vertical velocity distributions often conform to: (i) ‘law‐of‐the‐wall’ logarithmic theory; or (ii) profiles in the near‐bed region and within the transition to outer flow can be described using a log‐wake function. Consequently, for selected velocity profiles it is possible to derive hydraulic parameters suitable for input to incision models. Chezy‐C values are high, indicating low flow resistance, while bed shear stresses remain competent, even during low‐discharges, to transport cobble bedload across low roughness bedrock surfaces. Thus, as competence is high, no blanketing sediment deposits can develop within inner channels to prevent bedrock erosion. Consequently, within similar high competence systems, incision is probably progressive as long as sediment supply is sustained to abrade the bedrock. The landscape modelling implication is that abrasion in this system is supply‐limited and not limited by flow competence. In contrast, a transport‐limited system is likely to evolve to exhibit an alluvial bed. © 2018 John Wiley & Sons, Ltd.

A modified logarithmic spiral method for determining passive earth pressure

In this study, a modified logarithmic spiral method is proposed to determine the passive earth pressure and failure surface of cohesionless sloping backfill, with presence of wall–soil interface friction. The proposed method is based on a limit equilibrium analysis wherein the assumed profile of the backfill failure surface is a composite of logarithmic spiral and its tangent. If the wall–soil interface is smooth, a straight line does not need to be assumed for the failure surface. The geometry of the failure surface is determined using the Mohr circle analysis of the soil. The resultant passive earth thrust is computed considering equilibrium of moments. The passive earth pressure coefficients are calculated with varied values of soil internal friction angle and cohesion, wall friction angle and inclination angle, and sloping backfill angle. This method is verified with the finite element method (FEM) by comparing the horizontal passive earth pressure and failure surface. The results agree well with other solutions, particularly with those obtained by the FEM. The implementation of the present method is efficient. The logarithmic spiral theory is rigorous and self-explanatory for the geotechnical engineer.

QLog Solar-Cell Mode Photodiode Logarithmic CMOS Pixel Using Charge Compression and Readout.

In this paper, we present a new logarithmic pixel design currently under development at New Imaging Technologies SA (NIT). This new logarithmic pixel design uses charge domain logarithmic signal compression and charge-transfer-based signal readout. This structure gives a linear response in low light conditions and logarithmic response in high light conditions. The charge transfer readout efficiently suppresses the reset (KTC) noise by using true correlated double sampling (CDS) in low light conditions. In high light conditions, thanks to charge domain logarithmic compression, it has been demonstrated that 3000 electrons should be enough to cover a 120 dB dynamic range with a mobile phone camera-like signal-to-noise ratio (SNR) over the whole dynamic range. This low electron count permits the use of ultra-small floating diffusion capacitance (sub-fF) without charge overflow. The resulting large conversion gain permits a single photon detection capability with a wide dynamic range without a complex sensor/system design. A first prototype sensor with 320 × 240 pixels has been implemented to validate this charge domain logarithmic pixel concept and modeling. The first experimental results validate the logarithmic charge compression theory and the low readout noise due to the charge-transfer-based readout.

Logarithmic Ramifications of Étale Sheaves by Restricting to Curves

Abstract In this article, we prove that the Swan conductor of an étale sheaf on a smooth variety defined by Abbes and Saito’s logarithmic ramification theory can be computed by its classical Swan conductors after restricting it to curves. It extends the main result of Barrientos [7] for rank $1$ sheaves. As an application, we give a logarithmic ramification version of generalizations of Deligne and Laumon’s lower semi-continuity property for Swan conductors of étale sheaves on relative curves to higher relative dimensions in a geometric situation.

Unitarity problems in 3D gravity theories

We revisit the problem of the bulk-boundary unitarity clash in 2 + 1 dimensional gravity theories, which has been an obstacle in providing a viable dual two-dimensional conformal field theory for bulk gravity in anti-de Sitter (AdS) spacetime. Chiral gravity, which is a particular limit of cosmological topologically massive gravity (TMG), suffers from pertur- bative log-modes with negative energies inducing a non-unitary logarithmic boundary field theory. We show here that any f(R) extension of TMG does not improve the situation. We also study the perturbative modes in the metric formulation of minimal massive gravity- originally constructed in a first-order formulation-and find that the massive mode has again negative energy except in the chiral limit. We comment on this issue and also discuss a possible solution to the problem of negative energy modes. In any of these theories, the infinitesimal dangerous deformations might not be integrable to full solutions; this suggests a linearization instability of AdS spacetime in the direction of the perturbative log-modes.

Differential equations and logarithmic intertwining operators for strongly graded vertex algebras

We derive certain systems of differential equations for matrix elements of products and iterates of logarithmic intertwining operators among strongly graded generalized modules for a strongly graded vertex algebra under a certain finiteness condition and a condition related to the horizontal gradings. Using these systems of differential equations, we verify the convergence and extension property needed in the logarithmic tensor category theory for such strongly graded generalized modules developed by Huang, Lepowsky and Zhang.

Thermodynamic and magnetic properties of ferrofluids in external uniform magnetic field

The work is devoted to the theoretical investigation of the thermodynamic and magnetic properties of ferrofluids in applied magnetic field. Analytical expressions for the second and the third virial coefficients of dipolar hard spheres model were obtained by using the least-squares approximation to the simulation data (Elfimova et al., 2013 [4]). The expressions for the virial coefficients are presented as functions of the dipolar coupling constant λ and the Langevin parameter α . The analytical formulas for the virial coefficients were incorporated in to so-called logarithmic free energy theory (Elfimova et al., 2012 [8]). This theory yields the Helmholtz free energy and the magnetization. The comparison between theory and computer simulation shows good agreement for λ⩽2.The analytical expression of the Helmholtz free energy was also used to obtain a sedimentation equilibrium concentration profile of ferroparticles subjected to uniform magnetic and gravitational fields.

Vertex algebras associated to the affine Lie algebras of abelian polynomial current algebras

We construct a family of vertex algebras associated to the affine Lie algebra of polynomial current algebras of finite-dimensional abelian Lie algebras, along with their modules and logarithmic modules. These vertex algebras and their (logarithmic) modules are strongly [Formula: see text]-graded and quasi-conformal. We then show that matrix elements of products and iterates of logarithmic intertwining operators among these logarithmic modules satisfy certain systems of differential equations. Using these systems of differential equations, we verify the convergence and extension property needed in the logarithmic tensor category theory developed by Huang, Lepowsky and Zhang.

On logarithmic nonabelian Hodge theory of higher level in characteristic $p$

Given a natural number m and a log smooth integral morphism X\to S of fine log schemes of characteristic p>0 with a lifting of its Frobenius pull-back X'\to S modulo p^{2} , we use indexed algebras {\mathcal A}_{X}^{gp} , {\mathcal B}_{X/S}^{(m+1)} of Lorenzon-Montagnon and the sheaf {\cal D}_{X/S}^{(m)} of log differential operators of level m of Berthelot-Montagnon to construct an equivalence between the category of certain indexed {\mathcal A}^{gp}_{X} -modules with {\mathcal D}_{X/S}^{(m)} -action and the category of certain indexed {\mathcal B}_{X/S}^{(m+1)} -modules with Higgs field. Our result is regarded as a level m version of some results of Ogus-Vologodsky and Schepler.

Crystal thermoelasticity at extreme loading rates and pressures: Analysis of higher-order energy potentials

Several finite elastic strain measures are evaluated for use in constitutive models of crystalline elasticity and elasto-plasticity. These include the Green material strain tensor, the Eulerian material strain tensor, and the logarithmic material strain tensor, all of which are referred to locally relaxed coordinates invariant under spatial rotations. New applications of logarithmic strain-based theory towards shock compression of aluminum, copper, and magnesium single crystals and polycrystals are presented. Solutions to the planar shock problem from previous work are summarized and compared with the present results. Consideration of these new results in conjunction with previous analysis for a number of different metals, ceramics, and minerals suggests that Eulerian strain-based theory is most accurate for modeling the dynamic high-pressure response of ductile metallic crystals wherein ratios of elastic shear to bulk moduli tend to be relatively small, while logarithmic strain-based theory is recommended for modeling shocks in ceramics and minerals with larger ratios of effective elastic shear to bulk modulus.

Infinite class of PT-symmetric theories from one timelike Liouville Lagrangian.

Logarithmic timelike Liouville quantum field theory has a generalized PT invariance, where T is the time-reversal operator and P stands for an S-duality reflection of the Liouville field ϕ. In Euclidean space, the Lagrangian of such a theory L=1/2(∇ϕ)^{2}-igϕexp(iaϕ) is analyzed using the techniques of PT-symmetric quantum theory. It is shown that L defines an infinite number of unitarily inequivalent sectors of the theory labeled by the integer n. In one-dimensional space (quantum mechanics), the energy spectrum is calculated in the semiclassical limit and the mth energy level in the nth sector is given by E_{m,n}∼(m+1/2)^{2}a^{2}/(16n^{2}).

Universal parametrization of jet production based on parton and fragment rapidities

As the signature manifestation of QCD in high energy nuclear collisions jet production provides essential tests of that theory. But event-wise jet reconstruction can be complex and susceptible to measurement bias. And QCD theory in the form of Monte Carlo models of elementary collisions can also be complex and difficult to test. It may be beneficial to construct a simple static model of jet production in p-p collisions to facilitate data comparisons and model tests. QCD is a logarithmic theory featuring variations with energy scale of the form $\log(s/s_0)$. Jet-related data such as parton fragmentation functions plotted on logarithmic rapidities exhibit self-similar scaling behavior which admits simple and accurate parametrization with only a few parameters. In this study we extend that method to construct a parametrization of jet (scattered parton) momentum spectra based on certain measured logarithmic jet production trends. The parametrization is established with Sp\=pS jet data and then extrapolated for comparison with Tevatron and LHC jet data. In addition, the jet production model from the present study is combined with a parametrization of p-\=p fragmentation functions to predict the minimum-bias jet fragment contribution to hadron $p_t$ spectra. The prediction is compared with published p-p spectrum data to test the self-consistency of the model.

Study on hydraulic resistance of erodible bed at the Chiyoda experimental flume

Abstract. The authors made erodible bed experiments under steady flow condition at the Chiyoda Experimental Flume, a large-scale facility constructed on the floodplain of the Tokachi River, and observed sand waves on the bed of the flume. In this study, the characteristics of the sand waves are examined along the longitudinal survey lines and confirmed to be dunes. Next, the authors estimated Manning's roughness coefficients from the observed hydraulic values and assumed that the rise of the coefficients attributed to the sand wave development. Finally, vertical flow distribution on the sand waves are examined, and observed velocity distribution on the crest of waves found to be explained by the logarithmic distribution theory.

Analysis of shock compression of strong single crystals with logarithmic thermoelastic-plastic theory

A finite strain theory is developed for anisotropic single crystals undergoing shock loading. Inelastic deformation may arise from dislocation slip, twinning, or fracture and crack sliding. Internal energy can generally depend on a logarithmic measure of finite elastic strain, entropy, and an internal variable associated with defect accumulation. A closed form analytical solution is derived for the planar shock response in the thermoelastic regime, at axial stresses up to the Hugoniot elastic limit. In the plastic regime, for highly symmetric orientations and rate independent shear strength, the Rankine–Hugoniot conditions and constitutive relations can be reduced to a set of algebraic equations that can be solved for the material response. The theory is applied towards planar shock loading of single crystals of sapphire, diamond, and quartz. Logarithmic elasticity is demonstrated to be more accurate (i.e., require fewer higher-order elastic constants) than Lagrangian or Eulerian theories for sapphire, diamond, and Z-cut quartz. Results provide new insight into criteria for initiation of twinning, slip, and/or fracture in these materials as well as their strength degradation when shocked at increasingly higher pressures above the Hugoniot elastic limit.

Comparison theorems for Gromov–Witten invariants of smooth pairs and of degenerations

We consider four approaches to relative Gromov-Witten theory and Gromov-Witten theory of degenerations: Jun Li's original approach, Bumsig Kim's logarithmic expansions, Abramovich-Fantechi's orbifold expansions, and a logarithmic theory without expansions due to Gross-Siebert and Abramovich-Chen. We exhibit morphisms relating these moduli spaces and prove that their virtual fundamental classes are compatible by pushforward through these morphisms. This implies that the Gromov-Witten invariants associated to all four of these theories are identical.

Logarithmic two-point correlation functions from a z =2 Lifshitz model

Abstract The Einstein-Proca action is known to have asymptotically locally Lifshitz spacetimes as classical solutions. For dynamical exponent z = 2, two-point correlation functions for fluctuations around such a geometry are derived analytically. It is found that the retarded correlators are stable in the sense that all quasinormal modes are situated in the lower half-plane of complex frequencies. Correlators in the longitudinal channel exhibit features that are reminiscent of a structure usually obtained in field theories that are logarithmic, i.e. contain an indecomposable but non-diagonalizable highest weight representation. This provides further evidence for conjecturing the model at hand as a candidate for a gravity dual of a logarithmic field theory with anisotropic scaling symmetry.

Thermodynamics of ferrofluids in applied magnetic fields

The thermodynamic properties of ferrofluids in applied magnetic fields are examined using theory and computer simulation. The dipolar hard sphere model is used. The second and third virial coefficients (B(2) and B(3)) are evaluated as functions of the dipolar coupling constant λ, and the Langevin parameter α. The formula for B(3) for a system in an applied field is different from that in the zero-field case, and a derivation is presented. The formulas are compared to results from Mayer-sampling calculations, and the trends with increasing λ and α are examined. Very good agreement between theory and computation is demonstrated for the realistic values λ≤2. The analytical formulas for the virial coefficients are incorporated in to various forms of virial expansion, designed to minimize the effects of truncation. The theoretical results for the equation of state are compared against results from Monte Carlo simulations. In all cases, the so-called logarithmic free energy theory is seen to be superior. In this theory, the virial expansion of the Helmholtz free energy is re-summed in to a logarithmic function. Its success is due to the approximate representation of high-order terms in the virial expansion, while retaining the exact low-concentration behavior. The theory also yields the magnetization, and a comparison with simulation results and a competing modified mean-field theory shows excellent agreement. Finally, the putative field-dependent critical parameters for the condensation transition are obtained and compared against existing simulation results for the Stockmayer fluid. Dipolar hard spheres do not undergo the transition, but the presence of isotropic attractions, as in the Stockmayer fluid, gives rise to condensation even in zero field. A comparison of the relative changes in critical parameters with increasing field strength shows excellent agreement between theory and simulation, showing that the theoretical treatment of the dipolar interactions is robust.